Question: Simplify the following expression: $ x = \dfrac{-5}{8} - \dfrac{n + 10}{10n} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10n}{10n}$ $ \dfrac{-5}{8} \times \dfrac{10n}{10n} = \dfrac{-50n}{80n} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{n + 10}{10n} \times \dfrac{8}{8} = \dfrac{8n + 80}{80n} $ Therefore $ x = \dfrac{-50n}{80n} - \dfrac{8n + 80}{80n} $ Now the expressions have the same denominator we can simply subtract the numerators: $x = \dfrac{-50n - (8n + 80) }{80n} $ Distribute the negative sign: $x = \dfrac{-50n - 8n - 80}{80n}$ $x = \dfrac{-58n - 80}{80n}$ Simplify the expression by dividing the numerator and denominator by 2: $x = \dfrac{-29n - 40}{40n}$